generalformulationofastockpriceprocessthatfollowsthe
binomialisshownin FigureA12.3.Inthisfigure,Sisthe
currentstockprice;thepricemovesuptoSuwithprobability
pand down toSdwith probability 1 −pin any time period.
FIGURE A12.3General Formulation for Binomial Price Path
Creating a Replicating Portfolio
Theobjectiveinareplicatingportfolioistouseacombination
of risk-free borrowing/lending and the underlying asset to
createaportfoliothathasthesamecashflowsastheoption
beingvalued.Theprinciplesofarbitrageapplyhere,andthe
value of the option must be equal to the value of the
replicatingportfolio. Inthecaseof thegeneral formulation
justgiven,wherestockpricescanmoveeither uptoSuor
downtoSdinanytimeperiod,thereplicatingportfoliofora
call with strike price K will involve borrowing $B and
acquiring Δ of the underlying asset, where:
whereCu= Value of call if stock price isSu